Duncan's endorsement comes after the vice-president, Joe Biden, became the highest-ranking government official to back same-sex marriage on Sunday, telling Meet the Press he was "absolutely comfortable" with the issue. Obama has appeared reluctant to take up the issue in an election year but has said his views are "evolving" on the subject.

The comments by Biden and Duncan opened up speculation that the White House is moving towards a new position of support for gay marriage, beyond its already stated backing for civil unions.

But Obama's main political strategist, David Axelrod, played down the prospect of an imminent shift. In a conference call with reporters on Monday, he insisted that Biden's comments are consistent with those he expressed during the 2008 campaign.

Obama captured a large proportion of the gay vote during in 2008, but some disillusionment has crept in among campaigners since then. While the Obama administration has scrapped the policy of "Don't Ask, Don't Tell", which prevented gays serving openly in the military, it has made no moves on federal recognition for same-sex marriage. Obama also declined recently to sign equal employment rights into law by an executive order.

The president, reported by friends to be privately sympathetic to the case for gay marriage, has in public been keen not to alienate conservative religious voters and has stuck to a compromise worked out in 2008: favouring civil unions but not gay marriage.

Axelrod said Biden's comments were "entirely consistent with the president's position, which is that couples who are married, whether they are gay or heterosexual couples are entitled to the very same liberties". He added: "When people are married, we ought to recognise those marriages and afford them the rights to which they are entitled."

Axelrod, who held the conference call to highlight a new election ad by Obama, took the opportunity to contrast the president's position on gay rights with that of his Republican challenger, Mitt Romney.

He said Romney "has funded efforts to roll back marriage laws in California and other places" and "believes that we need a constitutional amendment banning the right of gay couples to marry and would take us backward not forward".

Biden's comments on Sunday and Duncan's remarks on Monday were quickly interpreted in some quarters as the start of an orchestrated campaign by the White House, foreshadowing a new position by Obama. But the more likely explanation is that Duncan, in a scheduled TV appearance, was simply questioned on the issue in response to Biden's remarks. Asked why he had not made his position public before, Duncan said no-one had asked him.

The debate comes as electors in North Carolina prepare to vote on an amendment to the state's constitution which would provide legal recognition only to marriage between a man and a woman.

The latest polling in North Carolina suggests the measure to effectively ban same-sex marriage and civil unions will pass on Tuesday, with a Public Policy Polling study showing that 55% of people are planning to vote for the the amendment and only 39% against.

More than 40 lesbian and gay couples are planning to request – and expect to be denied – marriage licenses in eight counties across North Carolina from Tuesday, protesting the proposed legislation. The protesters, from the Campaign for Southern Equality, argue that they live as "second-class citizens" in North Carolina.

Opposition to same-sex marriage in the state may offer some insight into why Obama is yet to pledge full support for full equal rights for same-sex couples. The president narrowly won North Carolina, which traditionally votes for Republican presidential candidates, in 2008, and the Democratic Party will hold its convention there in early September in a bid to take the state again.